Answer: Perfectly elastic supply of labor and downward sloping demand for labor is correct.
The firm in a perfectly competitive labor market is only a wage taker,accept the wage rate in the market just like as perfectly competitive firm. The market wage rate in a perfectly competitive market is the the firm's marginal cost of labor that the amount the firm should pay for each additional worker. The firm hires workers up to that point where marginal revenue product of last worker is equal to wage rate. So, there arises perfectly elastic supply of labor.
The demand for labor is downward sloping due to decreasing returns scale. As more workers employed, their productivity will diminish after certain point of time so demand for labor will decrease facing downward sloping demand.
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